⚡ Pluto.jl ⚡

2.3 s

Load data first

sounds filenames

7.2 μs

filenames

String1

"ow_runaway_melody.wav"

"ow_runaway_based_bass.wav"

"ow_runaway_full.wav"

1.6 μs

do some magic with filenames

8.4 μs

files

String1

"C:/data/projects/fft/fft-for-fun/data/ow_runaway_melody.wav"

"C:/data/projects/fft/fft-for-fun/data/ow_runaway_based_bass.wav"

"C:/data/projects/fft/fft-for-fun/data/ow_runaway_full.wav"

xxxxxxxxxx
 
files = map(
    name -> replace("$(normpath(joinpath(@__FILE__, "..", "..")))data/"*name,
            "\\" => "/"),
    filenames)

51.6 ms

parse and get acoustic samples

9.9 μs

parsed

Array{Float64,2}1

7578667×2 Array{Float64,2}:
  0.0         0.0
  0.0         0.0
  0.0         0.0
  0.0         0.0
  0.0         0.0
  0.0         0.0
  0.0         0.0
  ⋮           
 -3.05185e-5  0.0
  0.0         0.0
  0.0         0.0
  0.0         0.0
  0.0         0.0
  0.0         0.0

7578667×2 Array{Float64,2}:
 0.0  0.0
 0.0  0.0
 0.0  0.0
 0.0  0.0
 0.0  0.0
 0.0  0.0
 0.0  0.0
 ⋮    
 0.0  0.0
 0.0  0.0
 0.0  0.0
 0.0  0.0
 0.0  0.0
 0.0  0.0

7578667×2 Array{Float64,2}:
 0.0  0.0
 0.0  0.0
 0.0  0.0
 0.0  0.0
 0.0  0.0
 0.0  0.0
 0.0  0.0
 ⋮    
 0.0  0.0
 0.0  0.0
 0.0  0.0
 0.0  0.0
 0.0  0.0
 0.0  0.0

xxxxxxxxxx
 
parsed = [wavread(name)[1] for name in files]

7.5 s

due to documentation, the first returned value is the data

14.2 μs

15157334

xxxxxxxxxx
 
length(parsed[1])

0.0 ns

thats too l0ng sound, cut smth off

15157334 == 180 s.

336000 == 4 s.

24.4 μs

Array{Float64,1}1Float641

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

more335991

-0.0158086

335992

-0.0294809

335993

-0.0422376

335994

-0.0536515

335995

-0.0633564

335996

-0.0710776

335997

-0.0765404

335998

-0.0796228

335999

-0.0801721

336000

-0.0782495

2Float641

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

more335991

0.177801

335992

0.182562

335993

0.187231

335994

0.19187

335995

0.196448

335996

0.200964

335997

0.20539

335998

0.209754

335999

0.214057

336000

0.218268

3Float641

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

more335991

0.169225

335992

0.167547

335993

0.166234

335994

0.165471

335995

0.165441

335996

0.166265

335997

0.168035

335998

0.170843

335999

0.174718

336000

0.179662

x
 
begin
    sz = 336000
    shrink = [
        p[1:sz] for p in parsed
    ]
end

6.6 ms

x
 
sounds = (
    melody=shrink[1],
    bass  =shrink[2],
    full  =shrink[3]
);

0.0 ns

lets plot melody and bass waves

6.9 μs

x
 
plot([sounds.melody, sounds.bass], layout=2)

28.3 ms

and full, mixed up

13.5 μs

x
 
plot(sounds.full)

12.5 ms

now we can FFT

историческая справка: преобразование Фурье переводит содержимое *.wav файла в формат частот

15.2 μs

frequencies

Array{Complex{Float64},1}1Complex{Float64}1

-477.091+0.0im

8.17909+10.3384im

13.741-13.7773im

39.7332+5.69267im

38.8432+22.2648im

436.063+55.9534im

-66.8175-24.6853im

-58.0506+12.0036im

-77.6107-29.895im

-61.2397-43.885im

-346.667-104.775im

118.111+63.4176im

83.4279+7.41983im

83.3839+55.7542im

54.4538+59.9019im

236.742+128.816im

-140.092-119.287im

-85.1284-33.3887im

-63.0419-74.1623im

-30.0613-61.1259im

more335991

-346.667+104.775im

335992

-61.2397+43.885im

335993

-77.6107+29.895im

335994

-58.0506-12.0036im

335995

-66.8175+24.6853im

335996

436.063-55.9534im

335997

38.8432-22.2648im

335998

39.7332-5.69267im

335999

13.741+13.7773im

336000

8.17909-10.3384im

2Complex{Float64}1

110.218+0.0im

-73.4476+108.633im

50.9481+79.7494im

19.2993+44.5433im

-13.4279-47.5565im

42.2768-13.1802im

-51.8655+50.1493im

6.01922+96.6328im

7.93124+8.07052im

8.57625+5.82507im

-18.0226-76.9191im

61.1715-42.6003im

-3.09096-36.7624im

60.8627-31.3328im

-31.2472+42.665im

-13.5752+6.42453im

50.1979-63.631im

-11.8738-67.8499im

47.3329+12.3294im

-39.0646+67.1767im

more335991

-18.0226+76.9191im

335992

8.57625-5.82507im

335993

7.93124-8.07052im

335994

6.01922-96.6328im

335995

-51.8655-50.1493im

335996

42.2768+13.1802im

335997

-13.4279+47.5565im

335998

19.2993-44.5433im

335999

50.9481-79.7494im

336000

-73.4476-108.633im

3Complex{Float64}1

-93.569+0.0im

-78.5982+78.5635im

8.29198+61.0895im

4.13366+76.7825im

13.6396-13.4331im

249.701-7.06294im

-114.502+11.9929im

-67.6677+114.535im

-38.1666+29.696im

-3.55112-11.9985im

-188.544-151.948im

67.562-18.2989im

5.02278+0.71612im

107.843+19.7465im

3.45626+52.5325im

63.2231+44.0684im

-59.4847-98.5065im

-57.494-44.0637im

35.3528-17.5881im

-62.4256+11.9019im

more335991

-188.544+151.948im

335992

-3.55112+11.9985im

335993

-38.1666-29.696im

335994

-67.6677-114.535im

335995

-114.502-11.9929im

335996

249.701+7.06294im

335997

13.6396+13.4331im

335998

4.13366-76.7825im

335999

8.29198-61.0895im

336000

-78.5982-78.5635im

x
 
frequencies = fft.(shrink)

454 ms

draw melody and bass freqs separately..

примечание

рисуем в первых 10000 единиц времени, т.к судя по рисункам выше, 10к – это период функций, и дальше все поввторяется
рисуем модули чисел, т.к не хотим возиться с комплексными числами

30.8 μs

x
 
plot([abs.(frequencies[1]), abs.(frequencies[2])], layout=2, x_lims=(1, 10000))

75.0 ms

then draw the sum of melody and bass freqs..

9.0 μs

x
 
plot(abs.(frequencies[1] + frequencies[2]), x_lims=(1, 10000))

18.7 ms

and finally check on the result of FFT..

6.8 μs

x
 
plot(abs.(frequencies[3]), x_lims=(1, 10000))

25.4 ms

Таким образом, алгос:

Делаем преобразование Фурье песни
куча деталей и подводных камней
получаем набор частот
конец

2.8 ms